Mid-Air Haptic Textures

ABSTRACT

Described is a method for instilling the haptic dimension of texture to virtual and holographic objects using mid-air ultrasonic technology. A set of features is extracted from imported images using their associated displacement maps. Textural qualities such as the micro and macro roughness are then computed and fed to a haptic mapping function together with information about the dynamic motion of the user&#39;s hands during holographic touch. Mid-air haptic textures are then synthesized and projected onto the user&#39;s bare hands. Further, mid-air haptic technology enables tactile exploration of virtual objects in digital environments. When a user&#39;s prior and current expectations and rendered tactile texture differ, user immersion can break. A study aims at mitigating this by integrating user expectations into the rendering algorithm of mid-air haptic textures and establishes a relationship between visual and mid-air haptic roughness.

PRIOR APPLICATIONS

This application claims benefit to the following two U.S. provisional patent applications, all of which are incorporate by reference in their entirety.

1. U.S. Application No. 62/788,322, filed Jan. 4, 2019.

2. U.S. Application No. 62/945,272, filed Dec. 9, 2019.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to improved techniques for mid-air haptic-related interactions for textures.

BACKGROUND

The digitization of textured graphics has made huge strides and has enabled a wealth of applications. It is possible, for example, to search online databases via content-based image retrieval algorithms using graphics-only input features (rather than metadata and keywords). Graphics algorithms can then be fed with the search results and tasked with auto-generating massive photorealistic renders of virtual worlds. Physics engines that couple user interaction of these 3D worlds can then be used to synthesize textured audio creating an immersive multi-modal experience, minus the haptics.

When we search blindly through our pockets however, haptic information such as an object's compliance, the microgeometry of its surface and its friction properties is what allows us to quickly assess what's in there. Haptic technology has therefore been the focus of many research efforts in an attempt to render and communicate high fidelity textured tactile sensations. Wearable gloves, hand-held tools and vibrating electrostatic touchscreens are just a few examples of the currently available hardware contraptions capable of conducting texture information to the human haptic sensory system.

Further, mid-air haptics refers to the growing field of research that enables users to interactively touch and feel virtual objects and surfaces without having to wear or hold any specialized controllers. One prominent way of achieving this is to use ultrasonic phased arrays that electronically focus waves onto a user's hands and fingertips to create a vibro-tactile effect. Coupled with holographic visuals, mid-air haptics is a powerful tool to create immersive spatial interactions. For instance, one can feel a heart beating, hold the Earth, or remotely shake the hand of a distant collaborator. These interactions are intrinsically bi-modal, and while “seeing is believing, feeling is the truth”. Therefore, visuals and haptics are equally important in spatial interactions and must be holistically considered when designing multi-modal interfaces; if visual and haptic modalities were to convey discrepant information, user immersion would be under threat.

Displaying shape and texture information on a screen or in augmented and virtual reality (AR/VR) has been an active topic of research and development for many years, ever more so with the recent proliferation of machine learning and artificial intelligence (AI) approaches to graphic synthesis. Methods for the haptic and audio rendering of texture information are also well studied fields, at least for wearable, surface, and grounded haptic interfaces.

This has not, however, been the case with mid-air haptic technology since many other challenges had to be addressed first. About a decade ago Hoshi et al. showed that ultrasound could be used to induce haptic sensation. Building on this work, subsequent studies from various laboratories, have shown that ultrasound could be used to produce multi-point feedback, render 3D volumetric shapes, and could be used to convey emotional information. On that basis ultrasonic mid-air haptic technology has been studied in car user interfaces, AR collaborative workspace and enriching media and art applications. Despite this progress, further investigations in mid-air haptic perception are still needed to bridge the gap with graphical displays.

The accurate rendering of a virtual object, whether graphically or through touch technologies depends mainly on two components: its geometry (i.e. its shape) and its material properties (i.e. its texture). To that end, research in mid-air haptics is on-going with regards to mid-air haptic shape rendering algorithms, and still at its infancy with regards to texture rendering.

SUMMARY

In this application, we demonstrate how modulated focused ultrasound can be used to generate mid-air haptic textures given an image or graphic input. We seek to promote discussion in haptic mappings and their use in human-computer interaction (HCl) for mid-air haptic rendering of textures.

In this application, we also seek to take a leap forward in mid-air haptic texture rendering by presenting a novel approach to producing congruent image-based visuo-haptic mid-air textures. Our approach combines perceptual study results and machine learning to predict the visually perceived roughness of an image texture and use that to generate congruent mid-air haptic stimuli of an equivalent perceived roughness. Through the design of haptic stimuli based on visual texture information, we can thus avoid creating discrepant stimuli that would hinder the user experience.

To attempt to achieve our goal, we undertook three user studies. In the first study, we adopted a crowd-sourced approach in order to gather perceptual assessments of roughness in image textures when exposed only to visual stimuli. Based on these results, commonly applied statistical measures of image texture and machine learning techniques, we developed and trained an image processing algorithm that can successfully predict the subjective roughness for an image texture. In the second study, we explored the perception of roughness when individuals are exposed to mid-air haptic feedback only (i.e., without any other non-haptic stimuli). Using the data gathered from the second study, we determined a relationship between the draw frequency of mid-air ultrasonic haptic feedback and perceived roughness. Further, we hypothesized that both visual and tactile roughness perception could be matched, and therefore formulated an experiment to test this. Namely, we validated our approach in a third study by evaluating participants perception of texture when exposed to both visual and mid-air haptic stimuli. In this final study, participants were able to tune the tactile parameter of roughness in order to match the visual texture displayed on screen. The results demonstrate that participant parameters for visuals matched those predicted by our machine learning model, hence validating our approach.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying figures, where like reference numerals refer to identical or functionally similar elements throughout the separate views, together with the detailed description below, are incorporated in and form part of the specification, serve to further illustrate embodiments of concepts that include the claimed invention and explain various principles and advantages of those embodiments.

FIG. 1 shows a side view and a first-person view of a comparative demonstration of mid-air haptics-based textures.

FIG. 2 shows a schematic of a method for generating mid-air haptic textures.

FIG. 3 shows a schematic of an extraction of a displacement map from a tile graphic to produce a haptic effect.

FIG. 4 shows a schematic of a hand having exemplary illustration of collision points.

FIG. 5 shows a schematic of extracted features of a displacement map associated with a haptic mapping function block.

FIG. 6 shows a schematic of a system for generating mid-air haptic textures using an ultrasonic transducer array.

FIG. 7 shown is a graph comparing model predicted roughness values and observed median subjective roughness values from crowd-sourced data.

FIG. 8 is a linear regression of data in FIG. 7.

FIG. 9 is a graph showing a relationship between mid-air haptic frequency and its associated perceived roughness.

FIG. 10 is a linear regression conducted on observed value versus predicted values of study data.

Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of embodiments of the present invention.

The apparatus and method components have been represented where appropriate by conventional symbols in the drawings, showing only those specific details that are pertinent to understanding the embodiments of the present invention so as not to obscure the disclosure with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein.

DETAILED DESCRIPTION

I. Mid-Air Haptic Textures from Graphics

The ability for haptic technology to reproduce texture information has several enabling applications, including the touch of realistic virtual copies of valuable or historical items, robotic teleoperation for medical or industrial purposes, educational and training simulations in AR/VR, and forms a key part of human-fashion interaction (HFI); textural haptic information about products and fashion items can increase online purchase intention. The method of recording the haptic feel of a real object and later reproducing it for others to interact with is called haptography.

Hand-held Tools. Impedance-type haptic interfaces such as the SensAble Phantom Omni have long been the standard for rendering textures. Notable efforts include the Penn Haptic Texture Toolkit, a publicly available repository of hundreds of haptic texture and friction models, the recorded data from which the models were made, images of the textures, and even includes the code and methods necessary to render them on a Phantom Omni (or similar).

Wearables. There are an abundance of haptic gloves that are actuated via servos, pneumatics, voice coils, piezoelectric or other vibrotactile actuators. However, haptic systems have only recently started to be designed with mobility in mind, thanks to hardware miniaturization and advancements in battery technologies. Notable recent commercialization efforts include TACTAI and GoTouchVR.

Surface Haptics. There are three means of texture reproduction on touchscreens: moving overlays, ultrasonically vibrating surfaces, and electrostatic surfaces. When a user touches the screen, an overlay is actuated using motors to produce a shear force on the fingertip. Ultrasonic surface haptic devices vibrate the screen to reduce fingertip contact time thus reducing friction. Electrostatic haptic devices can form an electric field that attract the skin thus increasing normal force and friction.

Ultrasound Haptics. Signals driving a collection of ultrasonic speakers (or transducers) are modulated such that ultrasound waves interfere constructively at one or more focus points in space such that a tactile sensation is felt when touched by the bare hand of a user. This technology was first demonstrated in Japan in 2010 and commercialized by Ultrahaptics Ltd. in 2014. When a user touches a virtual object, the contact points between his or her hand and the object are recorded and one or more ultrasonic focus points can be made to ‘jump’ from point to point (in some order and speed) such that the object surface is felt. Varying the order, speed or waveform of the modulated ultrasound may simulate perceivable differences in textured effects, e.g., a faster hand traversal speed may be associated with a smoother surface, and a square modulated wave with a rougher one. This approach therefore creates a 1-to-1 mapping between a virtual object's shape and the projected haptic while allowing control of three haptic input parameters. Limitations of this technique include the unwanted side effect of audible noise, and blindness to graphical rendering of texture qualities.

A. Demo Contribution

Described herein are i) the introduction of a haptic mapping function ƒ and ii) its use to translate texture information from an input image or graphic into a haptic texture sensation in mid-air, thus iii) allowing for surface-free, tool-free, and wearable-free textured haptic feedback to dynamic touch interactions with AR/VR content. This approach is not a 1-to-1 bijection mapping since different images may ‘feel’ the same (i.e., it's a surjection). Moreover, the demonstrated approach is robust to any 2D or 3D image and can ‘see’ both macro- (e.g., the direction and width of gaps between kitchen tiles) and micro-features (e.g., differences in roughness between marble or ceramic tiles). Constructing the haptic mapping function requires much testing and calibration as it strongly depends on the haptic sensation it is applied to. In this application, we use the ‘circle’ haptic as this is currently the most studied one. We demonstrate the effectiveness of this process (see FIG. 2 below) by generating mid-air haptic texture sensations from an image database.

B. Demo Setup

Turning to FIG. 1, shown is our demonstration setup 100 composed of a 24″ LCD display, a laptop PC with mouse, and an Ultrahaptics Stratos Inspire (USI) device. The USI is ergonomically located below the display on a table. The USI uses a Leap Motion controller for hand-tracking, and 256 ultrasonic 40 kHz transducers arranged in a Fibonacci spiral (sunflower) pattern such that unwanted acoustic grating lobes are minimized.

Shown are the side view 110 and first-person view 120 of the demo where the user is exploring two different textures: bricks (left) and metal walkway (right). These are displayed on the screen and simultaneously projected onto the user's hands using the USI. Users can walk up and place their hands about 20 cm above the USI to feel the different textures displayed on the screen. Two textures are displayed side-by-side allowing for direct comparison. Users can also select different textures through a dropdown menu. The core demo features can be experienced in less than 1-minute.

C. Haptic Textures from Graphics

Turning to FIG. 2, shown is a schematic 200 of a method for generating mid-air haptic textures. An offline component 210 begins with image importation 220, proceeds to extract macro texture features Mi and micro texture features mi 230, and concludes with applying haptic mapping to sensation s_(i) where H[s_(i)]=ƒ(s_(i), m_(i), M_(i)) 240.

Further, using hand tracking 250, collisions with a virtual object x_(i) are detected 260. The center of mass of collision points X=μ(x_(i)) is calculated 270. The method takes in the output from the offline component 210 and projects haptic H[s_(i)] to X 280. The method then returns to hand tracking 250 and starts the process anew on an iterative basis.

Turning to FIG. 3, shown is a schematic 300 of the extraction of the displacement map 320 from a tile graphic 310 to produce a haptic effect 330. The tile graphic is taken from the CC0 Textures Online Library (https://cc0textures.com/) (accessed October 2018).

Turning to FIG. 4, shown is a schematic 400 of a hand 410 with exemplary illustration of collision points x_(i). These are holographic touches shown as points 440 on the index and middle fingers. The center of mass of the collision points X is shown as a point 430 on which a circle haptic s_(i) 420 is centered upon.

A displacement map allocates a grayscale value for pixels in a 2D image corresponding to height detail. These values are used to calculate the image micro- and macro-scale roughness (see FIG. 5, below).

Micro-Scale Roughness is calculated using the 2D autocorrelation function for a high-resolution image. This function establishes whether an image contains (non-)periodic features. For example, the autocorrelation function of a regular texture will contain peaks and valleys with spacings equal to the distance between the texture primitives. The autocorrelation function is most often obtained by taking the discrete Fourier transform (DFT) of the image and multiplying each coefficient with its complex conjugate before taking the inverse DFT. If the inverse DFT is not taken, the function obtained is the power spectral density (PSD) function that in this case measures the energy at each spatial scale. In addition, the PSD function can determine the coarseness of the texture, which we identify as micro-roughness. A cut-off frequency is determined first based on the hardware used and the scaling of the haptic texture. Fitting a slope to the higher frequency sections of the PSD function corresponding to frequencies above this cut-off gives us the roughness parameter we require. If the function rapidly decays then the image contains a smoother texture with texture information concentrated at lower spatial frequencies, whereas the image contains a rough texture if the function drops off slowly or flattens, indicating texture information at higher spatial frequencies. The micro roughness values (mRVs) learnt from the PSD function are then used to choose the circle haptic parameters from a look up table (LUT) that we have constructed a priori through user testing. The LUT maps an mRV to a ‘circle draw speed’ and haptic sample points which is projected onto the user's hands when 1) the hand is located within the bounds of the textured image, and 2) the hand has a velocity above a pre-defined threshold value (there is no texture sensation on a stationary hand). The corresponding haptic is projected at the center of mass X=μ(x_(i)), the average of all recorded collision points x_(i) on the user's hand, (see FIG. 4). We have also constructed a library of different LUTs for haptic sensations other than the circle.

Macro-Scale Roughness is closely coupled with the dynamic exploration of the textured surfaced. We achieve this by setting the circle haptic intensity to be proportional to the displacement map value at DM(X). Hence, the haptic intensity perceived by the user varies dynamically in strength according to the location of X, i.e., the main touch point of the user's hands with the graphic. The acoustic radiation force is due to the focused ultrasound. Therefore the strength of the haptic sensation is modulated between a minimum value corresponding to the vibrotactile threshold and the maximum output power of the USI.

Turning to FIG. 5, shown is a schematic 500 of extracted features of an image displacement map 510 associated with a haptic mapping function block 520. The haptic mapping function block 520 consists of an autocorrelation function 530 resulting in a micro-roughness draw frequency 550, and a gray-level function at X 540 resulting in macro-roughness intensity modulation 560. The autocorrelation of the displacement map is used to define micro-roughness parameters that control the draw frequency of a haptic pattern. The gray-level function at the dynamic touch position X is used to define macro-roughness parameters that control the ultrasound intensity level being outputted. Applying both micro- and macro-scale texture calculations simultaneously to mid-air haptic sensations (e.g., a circle tactile pattern) is what we call haptic mapping.

D. Further Study

Our procedure for rendering texture from graphics using mid-air ultrasonic haptics links dynamic exploratory touch with spatial variations in image graphic textures (both micro and macro features) and projects these rich tactile sensations directly onto the user's bare hands through an impinging ultrasonic pressure field

Turning to FIG. 6, shown is a schematic 600 of a system for generating mid-air haptic textures using an ultrasonic transducer array. Starting with a texture 610, texture information is extracted 630 and provided to the haptic mapping function 680. In parallel, a digital image 650 is taken from the texture 610 and digital hand-related information 640 is taken from features and movements of the hand 620. The digital image 650 and digital hand-related information 640 are processed via holographic interaction 660 and then provided to the haptic mapping function 680. The haptic mapping function 680 then generates the necessary signals for the ultrasound transducer array 690 to produce ultrasound generated texture 700 that is felt by the hand 620.

Thus, the method avoids possible sensory conflicts due to inconsistency between a haptic texture and its visual representation. Moreover, the method is robust against computer graphic rendering techniques (e.g., normal and bump maps) and can therefore be applied to a vast range of applications. Our demo provides insights towards the furthering of immersive AR/VR experiences with mid-air haptic textures, as well as the enabling opportunity for the substitution of real fabric textiles with ultrasonic replicas, what is effectively a step towards new HFIs paradigms where users of VR-dressing rooms and online shops can touch and feel digital haptic textures.

II. Predictive Model for Rendering Roughness in Visuo-Haptic Mid-Air Textures

This application proposes a new approach to generating mid-air haptic textures based on the visual representation of various materials. Our main contributions are the following: a) a model to predict perceived roughness from visual pictures; b) a method to translate perceived tactile roughness to mid-air haptic input parameters; and c) a user validated end-to-end algorithm capable of rendering mid-air haptic textures from visuals.

A. Introductory Concepts

Texture. Historically the word ‘texture’ (Latin ‘textura’) is related to that of woven fabric, appraised and appreciated through the sense of touch. Since then, the word has grown to become a highly global percept used more generally to describe the surface characteristics of an object which are distinct from its human-scale geometry. Because of this generalization however, there is little consensus as to what constitutes texture.

In fact, an assumed definition can only be obtained when an object's surface is discussed from the standpoint of the sensory system being used to transduce it. While texture is predominantly considered as a property that lies within the domain of touch, it is in fact multisensory. As such, texture can be separated into three distinct groups: visual texture, auditory texture, and tactile texture.

Texture contains numerous potential dimensions that traverse these three sensory modalities. For example: Shine/matte, coarse/fine, rough/smooth, hard/soft, or sticky/slippery. Some of these descriptors are applicable primarily to one specific modality, e.g. ‘shine’ is for vision, but ‘rough’ and many others may apply to multiple modalities. Across these different texture groups, researchers have attempted to provide definitions with varying success. A good example is that by Tamura et al. who attempted to define visual texture by stating: “We may regard texture as what constitutes a macroscopic region. Its structure is simply attributed to the repetitive patterns in which elements of primitives are re-arranged according to a placement rule”.

Just as texture is difficult to define as a concept, measures of perceived texture are also equally elusive. For example, while various features, such as surface element spacing and density of a homogeneous surface can be measured objectively using complicated apparatus, it is difficult to recreate their perceptual features. Similarly, while one can view the structure of a surface as a pattern arising from the repetition or randomness of smaller local sub-patterns and use these variances to discriminate between different types of textures, one cannot directly assign a subjective or perceptual label to them. Nonetheless, the measurement of sub-pattern features contributes heavily towards the assessment of a surface finish in the manufacturing purposes. Therefore, while these standardization efforts go as far as the reliable reproduction of a pattern, the relationship between these metrics and the subjective perception of texture is still not clear, and nor are those of the modality used.

Visual Texture Perception. General usage of the term ‘texture’ is most often associated with how an object feels when touched. However, humans often utilize visual observation to infer different material properties that comprise the surface of an object, most commonly referred to as ‘visual texture’. In fact, variations in visual texture heavily inform our interpretation of the world, and provide us with cues to understand the shape and orientation of a surface. Just as pattern variations in surface structure can lead to perceptually different tactile sensations, the human visual system also creates its own complimentary interpretation of these patterns.

Humans require the use of adjectives to interpret the various qualities found in texture in a natural and ubiquitous way, such as: roughness, directionality, contrast, and regularity. In particular, Tamura et al. has shown that coarseness, contrast, and directionality play a fundamental role in the visual interpretation of surface textures. However, the use of vague language to describe variations in visual texture may be interpreted very differently between individuals, affecting the consistency with which such subjective interpretations may be measured.

To that end, attempts have been made to associate human perceptual dimensions to quantifiable image attributes, such as roughness being related to the spatial size and density of texture primitives, known as texels. Furthermore, an alternative approach has been to vary pixel gray-level intensity throughout different local patterns within an image to elicit perceptually noticeable variations in texture dimensions. Considering the dimension of roughness specifically, four visual cues are commonly utilized. These are the proportion of image in shadow, the variability in luminance of pixels outside of shadow, the mean luminance of pixels outside of shadow, and the texture contrast.

In reality, texture is experienced as an entirely integrated sensation, where aspects of both visual and tactile modalities influence one's response to a texture. Previous work has identified that both these modalities operate in parallel, and feature consistency in interpretations of three textural dimensions: roughness, hardness, and slipperiness. With that being said, early work by Binns, showed that humans are capable of similar performance during texture classification whether using vision only or both vision and tactile modalities. With regard to singular dimensions, Lederman and Abbot demonstrated that texture roughness is perceived equivalently whether using vision, haptic or visuo-haptic modalities.

Tactile Texture Perception. The term ‘tactile texture’ relates to surface and material properties that are perceived by our finger upon contact with an object's surface. These can be a static (pressing down) or dynamic (sliding) tactile interaction. During the tactile exploration of an object and its surfaces, tactile qualities such as surface friction, roughness, and temperature are revealed. Moreover, different tactile dimensions are revealed depending on the type of tactile interaction one uses. As the hand/finger skin surface makes contact with an object's surface, the central nervous system is informed about the qualities of the contact. This influences our perception towards exploring, grasping, and manipulating our environment.

To that end, work by Okamoto et al. suggests there are three fundamental perceptual tactile dimensions. These are: roughness (rough/smooth), hardness (hard/soft), warmness (cold/warm). The perception of roughness can be further broken down into stickiness, and wetness (moist/dry). Research has also suggested that surfaces with grating wavelengths above 1 mm (macro) are perceived in a different fashion in contrast to surfaces with wavelengths below 1 mm (micro) therefore introducing a multi-scale element into texture perception.

While objects can be assessed visually (without making physical contact with the surface of an object) there is no way to obtain a full understanding of the shapes, textures, and materials that surround us by visual means alone. For example, seminal work by Katz, surmised that surface roughness cannot be estimated without the lateral motion between the object and the skin.

Roughness features are often classified in two levels (macro/micro) due to the different mechanoreceptors activated following either spatial or temporal stimulation during surface exploration. For coarse surfaces with many macro-scale roughness features, neuro-physiology studies have shown that the spatial distribution of SA1 (Merkel) receptor cells contribute to the perception of roughness, but the temporal information due to skin vibration during dynamic exploration of a surface does not. Conversely, for fine (micro) surface textures, motion is a necessary part of the haptic perception. Specifically, FA1 (Meissner) and FA2 (Pacinian) receptor cells are related to the perception of fine roughness, and require dynamic stimulation to perceive any micro-roughness features.

Visual Texture Analysis. Due to the many similarities between tactile and visual modalities in the assessment of roughness, we were motivated to study these in unison. Our approach thus involved extracting specific image texture features with which a subjective value of roughness could be predicted. Using this value, ultrasonic mid-air haptic feedback could then be tailored to produce a tactile equivalent sensation. Feature extraction from images has been a fastidiously researched area of computer vision, with numerous methods having been exploited (e.g., statistical, geometric, model-based).

Gray-level co-occurrence matrices are a commonly used statistical approach for image texture analysis due to their simplicity and easy interpretability. This method examines variations in pixel intensity values throughout an image across a given distance d and angle θ, to form a matrix with dimensions relative to the number of possible gray-levels contain within an image. The formulation of an image's gray-level co-occurrence matrices (GLCM) compiles both spatial and statistical information, and enables the computation of second order statistics, known as Haralick features. This approach has been widely adopted across various fields, such as, medical image analysis, object recognition from satellite imagery, and image classification tasks.

GLCM express the joint distribution probabilities that neighboring pixels occur within an image across relative polar co-ordinates (d, θ). For an image I with size (N×M) and p gray-levels, the (i,j)^(th) value within the resulting GLCM will express the number of times the i^(th) and j^(th) pixel values occur in an image when evaluated across the offset (d, θ).

A non-normalized GLCM can be computed as:

$\begin{matrix} {{{GLCM}_{{\Delta \; x},{\Delta \; y}}\left( {i,j} \right)} = {\sum\limits_{x = 1}^{N}{\sum\limits_{y = 1}^{M}{\wp \left( {x,y} \right)}}}} & (1) \\ {where} & \; \\ {{\wp \left( {x,y} \right)} = \left\{ {\begin{matrix} {1,} & {{{{if}\mspace{14mu} {I\left( {x,y} \right)}} = {{i\mspace{14mu} {and}\mspace{14mu} {I\left( {{x + {\Delta \; x}},{y + {\Delta \; y}}} \right)}} = j}},} \\ {0,} & {otherwise} \end{matrix},} \right.} & (2) \end{matrix}$

where x and y are the co-ordinate positions in image I, and I(x,y) indicates the pixel value at the relevant co-ordinate position. Selection of appropriate values for d can be difficult to infer, and misinterpretation of this value can lead to an incorrectly calculated matrix that does not capture the underlying structure of an image texture. However, Zucker and Terzopoulos document a strategy to overcome this by comparing matrices created over multiple spatial relationships and calculating the associated χ² value of each matrix. Higher χ² values reflect a value of d that more accurately captures the underlying structure of an image texture. An interesting caveat of this method is its robustness to image magnification.

In association with GLCMs are various second-order texture measures known as Haralick features. Haralick first proposed 14 types of feature statistics based on GLCMs. These can be split into 3 groups: Contrast, orderliness, and descriptives, as previous work has shown these groups to be independent of each other. Within the Contrast group, measures of contrast (CON), dissimilarity (DIS), and homogeneity (HOM)/inverse difference moment (IDM), exist to explain the relative depth and smoothness of an image texture at a given offset. Angular second moment (ASM), or energy (√ASM), and entropy (ENT), all contribute towards assessments of orderliness of pixel gray-level dispersion within an image texture. Descriptive measures are calculated on the entire 2-D matrix, offering first-order descriptive measures on the second-order spatial information captured during computation of an image's GLCM. Mean, standard deviation, variance, and correlation of matrix values can be computed within this group. In addition, the measures cluster shade and cluster prominence can be calculated to evaluate symmetry within the matrix.

Different Haralick feature combinations have been applied to measure image texture throughout numerous fields. Zhang et al. used ASM, CON, COR, and ENT for measuring texture from satellite imagery. Others have applied these features for the detection of cancers. We apply this approach to the HaTT image library in order to generate features for our prediction model training phase.

Tactile Texture Rendering. Rendering haptic virtual texture has focused many efforts in the haptic community and has been applied to many apparatus such as force-feedback devices, pin-arrays, vibrotactile actuators and an ultrasonic plate. Most of these approaches tune one or several output parameters to vary the perceived texture of the tactile stimuli. Among these parameters frequency and waveform have shown greater influence on the perceived tactile texture. It has been noted that exploration motion also plays an important role in texture perception. Therefore, researchers have been exploring the relationship between the feedback output and exploration motion speed, using pre-recorded data.

Moving from contact devices, few attempts at rendering tactile textures in mid-air have been made. Using an algorithm based on surface tessellation, Freeman et al. have been able to reproduce basic texture in mid-air. More recently, an algorithm extracting macro-roughness from graphics has been proposed. Using this information authors leverage bump-maps to produce virtual haptic textures in mid-air. In these bump maps, higher points have higher intensity, and lower points lower intensity. However, these studies focus on macro-roughness, as oppose to micro-roughness. To our knowledge, there are no studies investigating the perception of roughness in mid-air, even less combining it with visuals.

As one can see from our thorough literature review, vision and touch share 3 dimensions. In this application, we limit our scope to the main texture dimension, namely roughness. Additionally, we will focus on Visual and Tactile roughness, and exclude auditory roughness.

B. Understanding Subjective Visual Roughness

Our assumption underlying this work was that image data alone can be used to produce an equivalent haptic sensation that approximates the subjective level of roughness contained within a texture image. In order to explore this assumption, a visual texture database was required that had been subjectively assessed for the textural dimension of roughness. A suitable image database had to meet a number of prerequisite criterion, which were: 1. The data set must contain surfaces textures, 2. textures must contain a single homogeneous, or near homogeneous texture, 3. images must have been taken from a constant viewpoint, 4. images must be constantly illuminated, 5. must have been acquired from real surfaces, 6. images must contain a high enough resolution from which to capture exact detail, 7. data set must be sufficiently large (>50). Numerous image data sets were assessed, such as Brodatz, MIT Vision Texture (VistTex) database, PerTex database, Drexel database, and Penn Haptic Texture Toolkit (HaTT). Only the HaTT image data set appropriately met each requirement. However, 2 of the 100 images, (“playing card square.bmp” and “candle square.bmp”), were removed from the HaTT during this stage because these images violated our criteria.

Crowdsourcing Data Collection. Accurate perceptual assessments for a given data set are impinged on the collection of data from a sufficient number of observers. Traditional recruitment techniques, such as the recruitment of university students can prove difficult particularly for longer trials (>1 hr). In order to overcome this concern, we incorporated a crowd-sourced approach by utilizing Amazon's Mechanical Turk (AMT). The benefit of this approach was that a much larger user group could be obtained for a small monetary reward. 187 participants were recruited through AMT. Participants were first given a consent page to complete along with a description of what was required of them during the task. They were then presented with each of the 98 images consecutively in a randomized order. Their task was to rate each image across the textural dimension of roughness, as per Okamoto et al.'s description. Assessment of all 98 images was considered the entire Human Intelligence Task (HIT). Participants were given a maximum time limit of 3 hours to complete the task, as it was expected that the process may have taken an extended period of time, therefore a substantial time period was allowed, with the expectation that participants may have required breaks between roughness assessments. The mean time taken by users was 50 mins. Participants were required to be AMT Masters, have a HIT approval rating of >95%, and have over 1000 HITs approved. These caveats helped to minimize the risk of poor quality data being collected. In addition, a unique randomized ID was given at the beginning of the study that was to be entered upon completion of the study. This step acted as a validation method to ensure participants completed the HIT in its entirety. In return for their time, participants were rewarded with $7.40/hr, slightly over US minimum wage.

An absolute magnitude estimation procedure was applied during the subjective roughness assessment. No reference stimuli was first provided, instead participants were presented with a slider positioned below each image, with the adjectives “rougher” and “smoother” at each end point. No value range was provided, other than these adjectives. The goal was to establish individual participant ranges during their image roughness assessments.

Results. Efforts were taken to reduce the possibility of missing values for images, in the form of a response requirement before the next image in the set was displayed on screen. Participant data were cleaned if any image in the set was missing a roughness value. From the 187 initial responses, 114 were retained. Data for each participant was standardized across a range of 0 100, so their individual range for roughness was retained, but distributed evenly for all users. Data for each image were not normally distributed so median roughness values are reported and utilized throughout this work.

C. Perceptual Roughness Prediction Model

Having obtained a collection of perceptual data for the 98 images from HaTT data set, our ensuing task was to design and implement a prediction model that could successfully approximate a subjective value of roughness for any 2-dimensional image texture passed to it. While feeding an image's raw pixel values directly into a convolutional neural network (CNN) is a commonly adopted image processing method, particularly for classification tasks, we computed a series of additional features based on the computation of a GLCM. Our reasoning for this was that we wanted our network to learn associations on the underlying structure contained within the entirety of the image texture. To that end, our model takes as input several features collected through this processing step, in addition to the matrix itself and the pixel data from the image. The following sub-sections describe in detail each of our feature sets.

1. Feature Encoding

Image Feature Data. Texture images from the HaTT image data base were encoded as 24 bpp 1024×1024 bitmaps. We resized each image to 256×256 pixels, using a constant scale factor. Images were then converted to gray-scale and down sampled to 8 bits per pixel with anti-aliasing applied, in order to produce 256 gray levels. This processing step reduced file size and enabled a GLCM to be computed with size (2⁸)². This information was passed into our CNN as a 2D matrix with the shape 256×256, with height and width being 256, and gray-level set as 1.

GLCM Feature Data. GLCMs were computed for each image in the HaTT image data set. Firstly, an array of pixel distances (d=1, . . . , 20) were defined, and matrices were produced at each distance step across displacement vectors (θ=0°, 45°, 90°, 135°) respectively. Taking Zucker and Terzopoulos' approach to correctly build a matrix that represents the underlying structure contained within each image, we calculated χ² values for each matrix, and selected the matrix that produced the highest value for d. Once an appropriate value for d was established, we generated 4 matrices for each displacement vector. Transposed matrices were also created in order to represent relationships between pixels across the horizontal, vertical, and both diagonal directions. Summation of each matrix for a given value of θ and its transpose, as well as averaging between directions, allowed for the constructed GLCM to be symmetric and semi-direction invariant. Values were then normalized so that the resultant matrix contained the estimated probabilities for each pixel-co-occurrence. For our prediction model, this matrix was converted to a 3D matrix in the shape of 256×256×1, and passed as an input to a separate CNN with the same architecture as our image CNN.

Haralick features data. From the computation of each image's GLCM, a series of second-order statistical measures, known as Haralick features, could be calculated. To ensure our feature set contained independent variables, we computed features for the separate groups Contrast, Orderliness, and Descriptives. For the contrast group we selected the measure homogeneity (HOM) and energy (√ASM) for the orderliness group. We also computed mean, standard deviation, and maximum correlation coefficient (COR) for the descriptives group, and included cluster shade and prominence to assess symmetry in the GLCMs. As such, a total of 6 features were used as inputs to our model as a separate Multi-Layer Perceptron (MLP) network.

2. Model Architecture and Learning

In order to process both our GLCM and image, we constructed a network with 3 convolutional layers with Rectified Linear Unit (ReLU) activations, and He normal kernel initializers. The first convolutional layer applies a series of 16 7×7 filters to the image and GLCM, which is followed by a 4×4 max pooling layer to reduce the dimensionality of the image and GLCM data. Filter size is then reduced to a series of 16 3×3 in CNN layers 2 and 3. After CNN layer 2, another 4×4 max pooling layer is applied, with a final 2×2 max pooling layer after CNN layer 3. The subsequent output is then flattened and passed to a fully connected layer of 16-dimensions with ReLU activations, and L2 kernel regularization set to a value of 0.1 in order to minimize overfitting. This architecture was used for both GLCM and image feature data as separate input channels. Haralick feature data was processed using an MLP with 2 fully connected layers of 16-dimensions, and L2 kernel regularization applied to the second layer set to a value of 0.1, again to ensure overfitting was minimized. Each 16-dimension fully connected layer from the 3 models was then concatenated in order to return a single tensor passed to a fully connected layer with 3 dimensions and ReLU activations. The output layer generated used a sigmoid activation function in order to output a predicted value of subjective roughness in the range of 0-100. The model was trained using the mean absolute error (MAE) between the predicted values and observed median subjective roughness values obtained during our crowd-sourced data gathering exercise. The Adam optimizer with Nesterov momentum and a learning rate of 0.0005 was implemented, and a batch size of 1 applied. Our model was built using Tensorflow and the Keras API in Python and ran on a Nvidia GTX1070 GPU.

3. Model Performance

Using the scikit-leam API, we split our image data set (98 images) into separate train (80 images), validation (9 images), and test (9 images) sets, and trained our model over 150 epochs. Splitting our data set in this way acted as cross-validation to minimize over-fitting.

We examine how accurately our model could predict the observed median subjective roughness values obtained during our crowd-sourcing task. Our model achieved a mean absolute error (MAE) of 6.46 on our training set, and 9.73 on our validation set. Our model achieved a MAE of 4.246, mean squared error (MSE) of 35.6, and a mean absolute percentage error (MAPE) of 10.45% on the 9 images contained in our test set data.

Turning to FIG. 7, shown is a graph 700 displaying line plots 770 comparing model predicted roughness values (filled-in circles) and observed median subjective roughness values from crowd-sourced data (open circles). The x-axis shows various test image textures, including bubble envelope 740 a, silk 1 740 b, paper plate 2 740 c, brick 2 740 d, glitter paper 740 e, denim 740 f, cork 740 g, metal mesh 740 h, and plastic mesh 2 740 j. The y-axis 730 is a roughness value normalized from 0 to 100.

Turning to FIG. 8, shown is a graph 800 of a linear regression plot 810 between observed median subjective roughness values and predicted values 820 from our model. This linear regression was conducted to examine our model's goodness of fit. An R² value of 0.92, or 92% accuracy was observed in the model's predictions on test set data.

As a further assessment of our model's output, we conducted non-parametric analysis against our crowd-sourced median subjective visual roughness values for our test set data. As assessed by visual inspection of boxplots and Shapiro-Wilk tests, crowd-sourced subjective roughness ratings violated the assumption of normality (p<0.05 for all). A Spearman's rank-order correlation test was run in order to examine the relationship between the model's predicted values and the median observed subjective visual roughness values obtained during the crowd-source study. A statistically significant, very strong positive correlation between model output and observed visual roughness was found r_(s)(9)=0.929, p<0.001.

In order to explore further the accuracy of the model's predicted value of roughness in contrast to the entire distribution of values obtained during the crowd-sourcing study, we conducted one-sample Wilcoxon signed rank analysis on each individual image from our test data set. Table 1 displays the output from this analysis. Median values are reported for subjective visual roughness, as well as the IQR range, including Q1 and Q3. Predicted values are similar to distributions of crowd-sourced subjective roughness values for 5 of our 9 test set images, when assessed using Wilcoxon analysis.

Our model predicted a significantly higher subjective value of roughness for the texture image brick 2 than the median roughness value obtained during our crowd-sourcing study (difference=13.71, p<0.001). This was also the case for texture images metal mesh (difference=5.15, p<0.001), and plastic mesh 2 (difference=3.86, p=0.009). The prediction value for the image texture was significantly lower than the median roughness value for paper plate 2 (difference=−8.68, p<0.001). We speculate that our model did not achieve an even higher accuracy because human visual perception can be inherently inconsistent, as people have their own subjective experience in evaluating roughness. This inconsistency is reflected in some of the large inter-quartile ranges found in our crowd-source data set. As such, this makes it a challenging task to achieve perfect accuracy.

TABLE 1 Table 1: One-sample Wilcoxon test results on comparisons between visual roughness ratings, and model predicted roughness. The roughness range is normalized to lie between 0 and 100. Texture Name Visual Roughness Predicted Roughness Wilcoxon brick 2 M = 36.36, IQR = [20-63(43)] 50.07  <0.001 * bubble envelope M = 14.44, IQR = [6-30(24)] 14.66 0.153 cork M = 68.68, IQR = [45.8-89(43.2)] 65.49 0.431 denim M = 68.45, IQR = [55-82(27)] 68.34 0.944 glitter paper M = 61.39, IQR = [36-72(36)] 60.00 0.311 metal mesh M = 74.61, IQR = [51.1-89(37.9)] 79.76 <0.001  paper plate 2 M = 30.00, IQR = [17-53.6(36.6)] 21.32  <0.001 * plastic mesh 2 M = 74.71, IQR = [55-88.9(33.9)] 76.57  0.009 * silk 1 M = 28.16, IQR = [14-45.8(31.8)] 30.06 0.912

D. Mid-Air Haptic Roughness Perception

Having trained our model and tested its performance against our 9 image test data, our next step was to determine how a prediction of visual roughness could be applied to a mid-air ultrasonic haptic sensation. As discussed previously, frequency is one of the main parameters influencing tactile texture perception. Due to this we then sought to establish a relationship between mid-air haptic frequency and its associated perceived roughness.

The texture data used in this study were taken from a previous work (unpublished work accepted for publication) that explored user ratings of several scales of STM patterns. For this study, we only kept the circle with of perimeter 20 cm (i.e. 3.18 cm radius) and the associated roughness ratings.

The setup included an Ultrahaptics Evaluation kit (UHEV1) from Ultrahaptics Ltd. embedded at the bottom of an acrylic laser-cut black box. A squared hole on the top of the box let the participants received the mid-air haptic pattern on their palm.

A total of 11 participants rated the perceived roughness of 20 different frequencies: ranging from 5 Hz to 100 Hz with a 5 Hz step. Participants reported their answer using a Likert scale (1-9 from smooth to rough), presented on screen.

Turning to FIG. 9, shown is a graph 900 presenting the results for the 20 cm diameter circle. The x-axis 740 is the draw frequency and the y-axis 930 is the Likert scale. The plot includes the mean haptic 910 and standard error 920 of the roughness rating across a draw frequency.

From this graph, it was hypothesized that 25 Hz provides a significantly higher roughness than 75 Hz when displaying a circle of 20 cm. This result was confirmed in a second user study.

In this work, we are adding the hypothesis that the roughness ratings are linear on the range from 25 Hz to 75 Hz (R²=0.91). Therefore, we decided to use this range in our algorithm. In other word, for any roughness score predicted by our algorithm, we can attribute a single frequency value. This single frequency will be used to draw our mid-air haptic and conveyed the predicted level of roughness. We will see in the next section, how we validated this.

E. Visuo-Haptic Matching Task

In the previous section we presented the last steps of our design pipeline, i.e. the relationship between perceived roughness and mid-air haptic patterns property. Coupled with our work on inferring roughness from visuals, we now have all the pieces to render the haptic roughness. In this visuo-haptic matching task, we will validate our approach. More specifically we designed a study aiming at comparing our algorithm output with the user expected haptic texture.

1. Method

In this study, participants were adjusting the texture of a mid-air haptic pattern to match the texture from the visual displayed on the screen. We recruited 21 participants (10 female, 11 male, mean age: 33±7.8) in our office. Each participant was sat at a desk, with in front of them a computer screen displaying the visual texture. On the side, an Ultrahaptics UHEV1 device was producing a mid-air haptic circle with a perimeter of 20 cm. Participants hands were tracked using a Leap Motion controller, so that mid-air haptic patterns are always positioned in the center of their middle finger. During the study, participants were wearing headphones that generated pink noise, as to avoid any influence from auditory cues. Using a computer mouse, participants could change the mid-air haptic properties via a cursor displayed below the interface. Effectively, the cursor changed the draw frequency of the mid-air haptic pattern, yet the participants did not know this. Instead, the cursor was labelled as “rough/smooth”. Participants were instructed to change the haptic roughness until it matched that of the presented visual. After validation, the visuals were replaced with new visuals and participants repeated the task. In total, participants determined the haptic roughness of 9 visual stimuli. These visual stimuli were the same images as from our previous test-set (see Model Performance section). The study was approved by our internal ethics committee.

2. Results

As in the previous study, we examine how accurate our model could predict draw frequency, compare to the values obtained during the study. To achieve this a linear regression was conducted on observed value vs predicted values.

Turning to FIG. 10, shown is a graph 1000 with an x-axis 1020 of predicted values and a y-axis 1010 of observed values. The plot 1030 and predicted values 1040 display linear regression between determined median draw frequency values and predicted draw frequency values from our model. An R² value of 0.76 and a mean absolute error of 5.6 were observed.

Collected data from our validation were not normally distributed when assessed using their corresponding box plots and Shapiro-Wilk tests for normality (p<0.05 for all). Firstly, Spearman's rank-order correlation test was run so that the relationship between our model's predictions on haptic roughness could be evaluated against data captured during our visuo-haptic matching study. Similar to comparisons made between crowd-sourced median subjective roughness and predictions, a statistically significant, very strongly positive correlation was found between our model's prediction and participant's median haptic roughness assessments, r_(s)(9)=0.933, p<0.001.

It was critical to measure whether the estimation of mid-air haptic feedback varied in contrast to the visual only assessments of roughness captured during our crowd-source exercise. This information would provide an insight towards the feasibility that purely visual roughness information can be translated to the tactile domain using mid-air ultrasonic haptic feedback. Mann-Whitney U tests were run on comparisons between crowd-sourced visual roughness data and visuo-haptic roughness data. Data sets were different sizes, however Mann-Whitney testing is robust to unequal sample sizes. Additionally, values were scaled differently between data sets, therefore in order to draw any comparisons, visuo-haptic matching roughness values were transformed to fit the 0-100 range of the visual roughness scale. Table 2 shows median, and inter-quartile values for both haptic roughness data and visual subjective roughness data from our crowd-sourced study. Assessments of Mann-Whitney results demonstrate that 3 of the 9 images were similar during visual roughness assessment and visuo-haptic matching. Of the remaining 6 images, 4 of these (cork: p=0.008, denim: p<0.001, paper plate 2: p<0.001, and silk 1: p=0.009), visual assessments produced significantly higher perceived roughness values than during the visuo-haptic matching task. In contrast, the remaining 2 image textures, (metal mesh: p<0.001, plastic mesh 2: p=0.01), produced significantly lower values of perceived roughness than during the visuo-haptic matching task.

TABLE 2 Table 2: Mann-Whitney group differences between crowd-sourced subjective roughness data (0-100) and validation study haptic draw frequency data (scale transformed). Median, and IQR values are reported. Texture Name Haptic Roughness (Transformed) Visual Roughness Mann-Whitney brick 2 M = 28, IQR = [11-59(48)] M = 36.36, IQR = [20-63(43)] 0.051  bubble envelope M = 11, IQR = [2-22(20)] M = 14.44, IQR = [6-30(24)] 0.061  cork M = 62, IQR = [36-76(40)] M = 68.68, IQR = [45.8-89(43.2)]  0.008 * denim M = 56, IQR = [32-68(36)] M = 68.45, IQR = [55-82(27)] <0.001 * glitter paper M = 66, IQR = [42-76(34)] M = 61.39, IQR = [36-72(36)] 0.167  metal mesh M = 90, IQR = [78-96(18)] M = 74.61, IQR = [51.1-89(37.9)] <0.001  paper plate 2 M = 22, IQR = [11.5-34(22.5)] M = 30.00, IQR = [17-53.6(36.6)] <0.001 * plastic mesh 2 M = 82, IQR = [72-92(20)] M = 74.71, IQR = [55-88.9(33.9)] <0.010 * silk 1 M = 22, IQR = [10-32(22)] M = 28.16, IQR = [14-45.8(31.8)]  0.009 *

Finally, analysis of comparisons between data obtained during the visuo-haptic matching task and crowd-sourced visual roughness data using one sample Wilcoxon tests on each of the 9 test set images. Table 3 displays median, inter-quartile ranges, and Wilcoxon statistical values for each image. Comparisons showed that for 4 images, (brick: p<0.001, cork: p=0.038, denim: p<0.001, and silk 1: p<0.001), predicted haptic roughness from our model was significantly lower than haptic roughness during the visuo-haptic matching task. Moreover, predicted haptic roughness for 1 image, (metal mesh: p=0.005), was significantly higher than haptic roughness during the visuo-haptic matching task. All other comparisons, (bubble envelope, glitter paper, paper plate 2, plastic mesh 2) were similar.

TABLE 3 Table 3: One sample Wilcoxon signed rank test comparisons betwen median roughness (draw frequency ranging from 25 Hz to 75 Hz), and predicted roughness from our model. Median and IQR values are reported. Texture Name Haptic Roughness Predicted Roughness Wilcoxon brick 2 M = 61.00, IQR = [45.5-69.5(24.0)] 49.96  <0.001 * bubble envelope M = 69.50, IQR = [64.0-74.0(10.0)] 67.66 0.611 cork M = 44.00, IQR = [37.0-57.0(20.0)] 42.25  0.038 * denim M = 47.00, IQR = [41.0-59.0(18.0)] 40.82  <0.001 * glitter paper M = 42.00, IQR = [37.0-54.0(17.0)] 45.00 0.744 metal mesh M = 30.00, IQR = [27.0-36.0(9.0)] 35.12  0.005 * paper plate 2 M = 64.00, IQR = [58.0-69.25(11.25)] 64.38 0.763 plastic mesh 2 M = 34.00, IQR = [29.0-39.0(10.0)] 35.71 0.110 silk 1 M = 64.00, IQR = [59.0-70.0(11.0)] 59.97  0.001 *

F. Discussion

In this section, we further discuss the results of our work. We also take the opportunity to share some insights we discovered while carrying out our investigations.

1. Results

As reported above and in table 1, our algorithm predicts the subjective roughness of each picture with great accuracy (R²=0.926). The mean absolute error (MAE) is only of 4.25. Furthermore, the roughness ranking is respected between user ratings and algorithms predictions (Spearman's rank correlation coefficient=0.92). These values show that our model successfully predicts visual subjective texture.

However, one might note the high IQR for each of the textures and challenge these conclusions. Based on this observation and these insights, one may be tempted to further perfect the predictive model, or repeat the data collection process with a different methodology. These are valid options but looking closer at our data, one can argue and attribute this high IQR according to different factors, independent of our approach.

First, recall that our crowd-sourced study spanned an average over 50 minutes, which can lead to participants becoming less focused on the task towards the end of the study. With this decreased focus in mind, it is likely that the validity of their ratings decreased, too. However, we think that our high number of participants, and the fact that picture order was randomized, the effect of fatigue was limited. Another aspect to consider is the close resemblance between several of the textured images contained with the HaTT database. As discussed previously, constraints were applied to the image in order to facilitate the training of our predictive model. The resulting data set is therefore rather abstract and so subjective, and it is possible that it evoked slightly different sensations for each individual participant. In a way it is a phenomenon similar to abstract art, where two people that appreciate a particular artwork may have very different emotional responses and impressions regarding the same piece of art. Finally, texture, and especially roughness, is intrinsically an abstract notion whose subjectivity makes it difficult to grasp using a qualitative analysis such as these. It is not surprising that variation was obtained in the ratings. We develop this last point further in the next section. We would like to stress at this point that this result is a contribution on its own. While we applied this predictive model to mid-air haptics, the model could be applied to any other haptic devices capable of creating the tactile sensation of roughness.

In the evaluation study, we see a lower accuracy (R²=0.76), but error remains similar (MAE=5.65) and the rank order is still respected (r_(s)=0.933). A loss in accuracy was to be expected, as our predictive model was trained on visual ratings only, and not visuo-haptic ratings. Combining our predictive model with the roughness-to-draw-frequency relationship can only be as accurate as the two components taken separately. The Mann-Whitney test presented in table 2 explain further this drop in accuracy. In most cases, participants gave a roughness ratings significantly different in the visuo-haptic matching task than in the visual rating task.

The one-sample Wilcoxon signed rank test provides more details in our model accuracy (see Table 3). Indeed, according to the test results, 5 out of the 9 textures tested are significantly different. The fact that more than half of the predictions are significantly different than the participants ratings could be seen as a failure of our model. However, recall that the mean absolute error is only of 5.65 Hz and needs to be compared to the participants vibrotactile perceptual resolution. According to a review on psychophysical studies in haptic, the human just noticeable difference (JND) for vibrotactile frequency is around 3-30%. If we take the mean value and apply it to our range of frequency used in the study, we can deduce that in our case, human JND to haptic pattern is as big as 7.5 Hz. Since the human JND for vibrotactile feedback is greater than the mean absolute error of our model, it is unlikely that participants would be able to perceive them.

Finally, the low performance of our end-to-end algorithm could likely be explained in the rendering method used for our mid-air haptics stimuli. As said in the literature review, the two main parameters in vibrotactile stimulations influencing texture perception are frequency and waveform. In the current study, we used only frequency. It is likely that varying the waveform will allow for finer tuning of the perceived tactile roughness. However, further investigations would be required for establishing a new relationship between perceived tactile roughness and both frequency and waveform. We defer this for future work since the results reported herein are in our opinion promising and of interest to the community and could already be implemented in real world applications.

2. Insights and Limitations

We noticed that roughness ratings were not normally distributed from rough to smooth. Indeed, both in the visual ratings and the validation task, participants tend to give ratings that tend either towards rough or smooth, but not in-between. This might be due to the existing dichotomy in our language. In the English language, there are no adjectives describing different level of roughness. A material is either rough or smooth.

From this observation, one could hypothesize that roughness accuracy in the tactile part is not that important. According to modality appropriateness it is likely that the main texture judgement comes from visual cues as opposed to tactile ones, as vision possess greater spatial acuity. Therefore it is fine to limit tactile roughness to a limited amount of levels spreading from rough to smooth. Provided comparative assessments between two materials with similar perceptual assessments of roughness, such an approach is viable. This has great implications for modem day applications, while research in mid-air haptic texture rendering closes the gap with visual texture rendering.

Finally, we would like to note that one limitation of our approach is that we only focus on texture roughness among all other possible dimensions of texture. More specifically we discuss micro-roughness prediction and rendering, and omit macro-roughness, which encompasses the elements with spatial resolution greater than a finger pad. Of course, one would expect that adding more texture dimensions to our model could increase realism and probably accuracy too. However, the approach described here could easily be applied to those dimensions as well. Addressing all three texture dimensions shared between vision and touch would have to extend beyond the scope of this paper, which has mostly focused on the proposed methodology, and its corresponding user validation, for the predicting and rendering of congruent visuo-haptic textures in mid-air.

G. Further Study

In this application, we have shown that visual texture roughness can correctly be predicted using our machine learning approach with 92% accuracy. Using results from perceptual studies, we have established a relationship between tactile roughness and mid-air haptic input parameters. Combining these, our approach was then shown to be able to predict the visual perceived roughness of a picture and use this prediction to generate the corresponding mid-air haptic input parameters that an ultrasound phased array device can interpret and output haptic feedback stimuli onto a user's hands. We have validated our approach via a user study and showed that our predictive model for rendering roughness in visuo-haptic setting was accurate at 76%. To the best of our knowledge, this is the first attempt to unify visual texture perception with that achieved by ultrasound mid-air haptic displays. In future work, we will expand our algorithm by enabling extra texture dimension to be predicted and conveyed through mid-air haptic technology. As discussed previously, such dimensions could include macro-roughness or hardness. We will also aim at assessing the benefits of our approach towards improving the user experience during spatial interaction with digital environments. To that end, one could imagine implementing our approach, or an improved iteration of it, in applications such as e-textiles in AR and VR thus opening up new possibilities in the field of human-fashion interaction (HFI).

III. Expressing Tactile Expectations of Visual Textures Via Mid-Air Haptic Feedback

Prior research has established congruences in texture perception between human visual and haptic modalities. In reality, texture is perceived as an entirely integrated sensation, where aspects of both visual, tactile and auditory modalities influence one's response to a texture. Drawing on the utility of integrated multi-modal feedback, we propose a method that incorporates visual texture information to produce both haptic and auditory feedback. This procedure aims to produce entirely congruent multi-modal digital texture renderings, akin to those experienced in the real world.

A. The Method

As an overview, the method features an initial step which is the design and training of a visual texture dimension machine learning prediction and classification model. Secondly, a linear regression process is conducted in order to match visual texture dimension prediction values to specific haptic sensation attributes that have been validated to produce a particular haptic texture dimension. This procedure forms our haptic prediction model. Finally, utilizing the classification data for the associated visual textures, we develop an audio database and an associated rendering method to produce dynamic auditory feedback that is tied to the visual features within a texture image. Each step is detailed below.

1. Visual Texture Prediction Pre-Processing and Feature Extraction

As a preliminary step, this method first features a set of image textures (currently 98), of size 1024×1024 pixels (24 bits per pixel). These images are assessed by human users subjectively, and values of 0-100 are given for each of the following texture dimensions: roughness, bumpiness, hardness, stickiness, warmness. This stage also requires image data to be labelled, in order to assign each image to a specific texture group (‘paper’, ‘wood’, etc). This process can be done via crowdsourced means such as Amazon's Mechanical Turk (AMT).

Following this procedure, data is assessed, cleaned, outliers are removed, then mean and standard deviation (or median and +−inter-quartile range) values are retained for each of the texture dimensions. This data is utilized for training and validation in subsequent steps.

Next, the image data set is subject to several pre-processing steps. Firstly, images are converted to gray-scale, and resized to 256×256 pixels (8 bit-per-pixel), using constant scaling. Next, gray-level co-occurrence matrices (size 256×256) are calculated for a series of displacement vectors: distances (1, 2, 3, 4, 5, 6, 7, 8, 9, 10), and angles (0, 45, 90, 135). Once each matrix is calculated, a Chi-Square test is conducted on each of the matrices, and the displacement vector that produces the highest value is selected. This step is conducted in order to determine which displacement vector correctly identifies the structure within the image texture, allowing both the spacing and direction of the texture structure to be obtained.

Once a correct distance value is obtained, matrices for all angles (0, 45, 90, 135) are constructed. For a given angle, transposed matrices are also constructed in order to represent the relationship between pixels across the horizontal, vertical, and both diagonal directions. Matrices for the correct distance values and a given angles, plus each transpose matrix are summed and averaged in order to produce a symmetric and semi-direction invariant matrix. Values are then normalized so that the resultant matrix contains the estimated probabilities for each pixel co-occurrence.

Once this matrix has been produced, further second-order statistical measures are obtained, known as Haralick features. This feature set contains 3 distinct groups: Contrast, Orderliness, and Descriptives. We select singular values for each group, in order to ensure each texture measure was independent. Homogeneity is selected for Contrast, which produces a value between 0-1. This feature measures how close the distribution of elements in the GLCM are to the diagonal of the GLCM. Entirely diagonal gray-level matrices give a homogeneity of 1, and this value becomes large if textures contain only minimal changes in pixel values. Energy is selected as the Orderliness descriptor, where Energy is the square root of the matrix Angular Second Moment. Energy is a 0-1 value, where 1 represents perfectly ordered pixel co-occurrences. For the Descriptives group, we select the GLCM Mean, Variance, and Maximum Correlation Coefficient. In addition, the metrics Cluster Shade, and Cluster Prominence are included to measure the symmetry in each GLCM. The final output of this process is a set of 8 features that characterize the texture contained with a given image.

2. Visual Texture Prediction Model Architecture

In order to process both the GLCM and images, a network with 3 convolutional layers with ReLU activations, and He normal kernel initializers is constructed. The first convolutional layer applies a series of 16 7×7 filters to the image and GLCM, which is followed by a 4×4 max pooling layer to reduce the dimensionality of the image and GLCM data. Filter size is then reduced to a series of 16 3×3 in CNN layers 2 and 3. After CNN layer 2, another 4×4 max pooling layer is applied, with a final 2×2 max pooling layer after CNN layer 3. The subsequent output is then flattened and passed to a fully connected layer of 16-dimensions with ReLU activations, and L2 kernel regularization set to a value of 0.1 in order to minimize overfitting. This architecture is used for both GLCM and image feature data as separate input channels. Haralick feature data is processed using an MLP with 2 fully connected layers of 16-dimensions, and L2 kernel regularization applied to the second layer set to a value of 0.1, again to ensure overfitting is minimized. Each 16-dimension fully connected layer from the 3 models is then concatenated in order to return a single tensor passed to a fully connected layer with 3 dimensions and ReLU activations. The output layer generated uses a sigmoid activation function in order to output a predicted value of subjective roughness in the range of 0-100. The model is trained using the mean absolute error (MAE) between the predicted values and observed median subjective values obtained during the initial texture classification and dimension estimation exercise. For training, the Adam optimizer with Nesterov momentum and a learning rate of 0.0005 is implemented, and a batch size of 1 applied.

The same general architecture is applied in order to classify textures into specific groups. The primary difference is that group data is used as the dependent variable, as opposed to texture dimension mean/median values. In addition, the fully connected layer after concatenation utilizes ‘softmax’ activations. Furthermore, the output layer is no longer a sigmoid activation function, but rather categorical cross entropy is used.

3. Haptic Texture Prediction Model

Based on the output from the visual texture dimension prediction model, 0-100 values can be rendering using the Ultrahaptics mid-air haptic device. In the context of ‘roughness’, we convert a given prediction value to the draw frequency of a haptic sensation using a linear regression approach. The association of sensation draw frequency and haptic roughness has been validated using a perceptual user study. We map the image prediction scale (0-100) to the range of draw frequencies that define sensations between ‘rough’ and ‘smooth’. This method can be extrapolated for additional texture dimensions.

B. Texture Classification and Auditory Feedback Associations

We propose that by training the Visual Texture machine learning model to output a group value for a given image texture, we can associate this output with a library of audio files, or synthesis parameters, for each texture group. This enables auditory feedback for an image texture, which can be further modulated via an image normal map. Firstly, a database of audio files can be referenced. In addition, appropriate parameters for an audio synthesis method (additive, subtractive, modal) can be obtained following the classification step. Utilizing an image normal map enables audio intensity and frequency modulation based on variations in the local features contained within each image texture. These sounds would be produced at the point of contact with a virtual texture and can be rendered via parametric audio via the Ultrahaptics mid-air device, or alternatively headphones may be used.

IV. Conclusion

While the foregoing descriptions disclose specific values, any other specific values may be used to achieve similar results. Further, the various features of the foregoing embodiments may be selected and combined to produce numerous variations of improved haptic systems.

In the foregoing specification, specific embodiments have been described. However, one of ordinary skill in the art appreciates that various modifications and changes can be made without departing from the scope of the invention as set forth in the claims below. Accordingly, the specification and figures are to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of present teachings.

Moreover, in this document, relational terms such as first and second, top and bottom, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms “comprises,” “comprising,” “has”, “having,” “includes”, “including,” “contains”, “containing” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises, has, includes, contains a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by “comprises . . . a”, “has . . . a”, “includes . . . a”, “contains . . . a” does not, without more constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises, has, includes, contains the element. The terms “a” and “an” are defined as one or more unless explicitly stated otherwise herein. The terms “substantially”, “essentially”, “approximately”, “about” or any other version thereof, are defined as being close to as understood by one of ordinary skill in the art. The term “coupled” as used herein is defined as connected, although not necessarily directly and not necessarily mechanically. A device or structure that is “configured” in a certain way is configured in at least that way but may also be configured in ways that are not listed.

The Abstract of the Disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, various features are grouped together in various embodiments for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed embodiment. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separately claimed subject matter. 

We claim:
 1. A method for generating mid-air haptic textures comprising: importing a texture image having macro texture features Mi and micro texture features mi by an offline component; extracting, by the offline component, Mi and mi from the texture image and applying haptic mapping to sensation si where H[si]=f(si, mi, Mi) to generate an offline component output; on a iterative basis: a) detecting, by a mid-air tracking system, collision points between a moving human hand and a virtual object xi; b) calculating, by the mid-air tracking system, the center of mass of the collision points X=μ(xi); c) establishing, by the mid-air tracking system, projecting H[si] to X depending in part on the offline component output.
 2. The method as in claim 1, wherein the center of mass of the collision points is not on the human hand.
 3. The method as in claim 1, wherein extracting Mi and mi from the texture image uses a displacement map.
 4. The method as in claim 3, wherein extracting Mi and mi from the texture image avoids possible sensory conflicts due to inconsistency between the mid-air haptic texture and its visual representation.
 5. The method as in claim 3, wherein mi is calculated using a 2D autocorrelation function for a high-resolution image.
 6. The method as in claim 5, wherein the 2D autocorrelation function establishes whether an image contains periodic features.
 7. The method as in claim 5, wherein the 2D autocorrelation function is obtained by taking a discrete Fourier transform of the texture image and multiplying each coefficient with its complex conjugate before taking an inverse discrete Fourier transform.
 8. The method as in claim 5, wherein the 2D autocorrelation function is obtained by a power spectral density function that measures energy at each spatial scale.
 9. The method as in claim 3, wherein Mi is calculated by setting a circle haptic intensity to be proportional to the displacement map value at DM(X).
 10. The method as in claim 9, wherein strength of a haptic sensation is modulated between a minimum value corresponding to a vibrotactile threshold and a maximum output power of a mid-air haptic generator.
 11. A method of rendering roughness in visuo-haptic mid-air textures, comprising: (1) forming a haptic prediction model by: (a) training a visual texture dimension machine learning prediction and classification model; (b) calculating a linear regression process to match visual texture dimension prediction values to validated specific haptic sensation attributes to produce a particular haptic texture dimension; (2) using the prediction and classification model for the visual texture dimension prediction values, developing an audio database and an associated rendering method to produce dynamic auditory feedback that is tied to visual features within a texture image.
 12. The method of claim 11, wherein training a visual texture dimension machine learning prediction and classification model comprises obtaining image texture data based on the subjective observations of a plurality of test subjects.
 13. The method of claim 12, further comprising: converting the image texture data to grayscale using constant scaling.
 14. The method of claim 13, further comprising: calculating gray-level co-occurrence matrices for a plurality of displacement vectors.
 15. The method of claim 14, further comprising: calculating matrices for correct distance values and pre-determined angles; summing and averaging transpose matrices to produce a symmetric and semi-direction invariant matrix that is normalized so as to contain estimated probabilities for each pixel co-occurrence.
 16. The method of claim 11, wherein calculating a linear regression process uses a network with convolutional layers with Rectified Linear Unit activations and He normal kernel initializers.
 17. The method of claim 16, further comprising generating an output layer using a sigmoid activation function to output a predicted value of subjective roughness.
 18. The method of claim 11, wherein using the prediction and classification model for the visual texture dimension prediction values comprises converting a prediction value to a draw frequency of a haptic sensation using a linear regression approach.
 19. The method of claim 11, wherein dynamic auditory feedback that is tied to visual features within a texture image includes using audio intensity and frequency modulation based on variations in local features contained within the image texture.
 20. The method of claim 19, further comprising: rendering the dynamic auditory feedback via parametric audio. 